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Zhi-Wei Sun's Conjecture 3.4 on a Truncated Legendre-Symbol Determinant

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zhi-wei-sun-legendre-determinantNumber theoryposed by Zhi-Wei Sunrecorded: solved

1 attempt · no person has looked

Statement

Zhi-Wei Sun conjectured a closed evaluation of a truncated Legendre-symbol determinant. For every prime p≡3(mod4)p \equiv 3 \pmod 4 it equals ⌊(p−2)/3⌋2x\lfloor (p-2)/3 \rfloor^2 x, proved by reducing to inverse data for Chapman's full Legendre-symbol matrix and evaluating that with Vsemirnov's factorization and a Schur-Pfaffian resolvent identity.

Context

One of Zhi-Wei Sun's numbered conjectures on Legendre-symbol determinants, a well-defined target with a small dedicated following.

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  • #1

    Attempt 1

    proof attemptChatGPT with Yaoran Yang, Gaishi Yang, Yutong Zhang ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    ChatGPT
    people
    Yaoran Yang, Gaishi Yang, Yutong Zhang

    The abstract states flatly that OpenAI's ChatGPT produced the proof, which the authors independently checked and confirmed. The authors separately used a GPT-assisted framework to develop Lean 4 formalizations of selected components.

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